Set X consists of all prime numbers less than 60. Set Y consists of al

Question

Set X consists of all prime numbers less than 60. Set Y consists of all integers which have a remainder of 2 when divided by 7. How many integer values are part of both sets?

A. None
B. One
C. Two
D. Three
E. Four

harshitagarg · Answer

The official explanation provided is:
If the members of Set Y have a remainder of 2 when divided by 7, this means that they are each 2 more than a multiple of 7. Therefore, the members of Set Y are {9, 16, 23, 30, 37, 44, 51,58, …} The only members of Set Y that are prime numbers less than 60 are 23 and 37.

The correct answer is choice C.

CAN ANYONE CLARIFY WHY IS 2 NOT INCLUDED IN SET Y? THE REMAINDER WHEN 2 IS DIVIDED BY 7 IS 2 SO IT SHOULD BE INCLUDED IN THE SET?

jazyb · Answer

prime nos set X =

Now divide by each number by 7 and see what the remainder is. 23-7*3=2, 37-7*5=2, so set Y has  . 
Only 2 numbers are common in set X and Y, so answer is C.

MikeScarn · Answer

I agree with you my friend.  2 is a prime number  and  \frac{2}{7}  = 0 remainder 2

Therefore, I believe the answer should be  D. Three

Set X:  2 , 3, 5, 7, 11, 13, 17,  23 , 29, 31,  37 , 41, 43, 47, 53, 59
Set Y:  2 , 9, 16,  23 , 30,  37 , 44, 51, 58, 65.....

jazyb · Answer

I believe because result of  \frac{2}{7}  is not an integer.

AliciaSierra · Answer

Bunuel , Need your expert advice please. How answer is C. As per me Answer should be D as 2,23,37 will be common terms

Bunuel · Answer

Primes less than 60:  2 , 3, 5, 7, 11, 13, 17, 19,  23 , 29, 31,  37 , 41, 43, 47, 53, 59. (17 primes)
Integers which have a remainder of 2 when divided by 7:  2 , 9, 16,  23 , 30,  37 , 44, 51, 58, ...

There are three numbers in common of these two sets.

Answer: D.

AliciaSierra · Answer

OA says C

Bunuel · Answer

_________________
OA is wrong. Edited.

hovhannesmkrtchyan · Answer

What about number 2?

If we write X = qXd+r and substitute q = 0,1, 2, 3, 4, ..... , then we would get X = 2, 9, 16, 23.... .
And number 2 is the smallest even prime number? So, why isn't 2 involved in the set ?

Bismarck · Answer

OA: D

Set X :{ 2 , 3, 5, 7, 11, 13, 17, 19,  23 , 29, 31,  37 , 41, 43, 47, 53, 59}
Set Y :{ 2 , 9, 16,  23 , 30,  37 , 44, 51, 58,..............}

3  integers i.e  2,23,37  are part of both the sets.

HarshavardhanR · Answer

Here, rather than list down all the prime numbers less than 60, it may be quicker to identify all the prime numbers less than 60 in Set Y.

Set Y -> 2, 9, 16, 23, 30, 37, 44, 51, 58,......

How many prime numbers in Set Y that are less than 60?

{2, 23, 37} --- 3.

Thus, the answer is 3.

---
Harsha

Set X consists of all prime numbers less than 60. Set Y consists of al

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Set X consists of all prime numbers less than 60. Set Y consists of al

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